Fatigue behaviour and constitutive model of yellow sandstone containing pre-existing surface crack under uniaxial cyclic loading

In engineering practice, rock masses are often subjected to cyclic loading. Under cyclic loading, the mechanical properties of rocks are significantly different from those under conventional loading conditions. The mechanical behaviour and fatigue of intact rock has been extensively studied. However, the mechanical fatigue properties of rock masses with surface cracks and related damage evolution models are not well understood. In this study, a series of fatigue damage tests were carried out on yellow sandstone specimens; five different pre-existing surface crack angles (0 degrees, 15 degrees, 30 degrees, 45 degrees and 60 degrees) and three different maximum cyclic stress levels (19.1 MPa, 25.6 MPa and 30.3 MPa) were considered. The results showed that with the increase in the number of cycles, Young's modulus gradually stabilized, while the secant modulus decreased non-linearly. The maximum strain and residual strain continuously accumulated. The influence of macro cracks on the damage of rocks was studied through the increase in strain energy. Based on the macro-micro coupling damage, a constitutive model was proposed for the fatigue test. The theoretical results were fitted with the experimental data, showing that the proposed model can effectively describe the fatigue damage characteristics of fractured rock masses. The research results have certain reference value for the long-term stability evaluation in fractured rock mass engineering.